What is prime and composite numbers?

Why it matters

Primes are the building blocks of every other whole number — every composite breaks down into a unique product of primes (its prime factorization). This sets up greatest common factor, least common multiple, and simplifying fractions, all of which dominate Grade 4-6 math.

Worked example

Is 12 prime or composite? Is 13 prime or composite?

1. 1

   Start with 12. List its factors — all the whole numbers that divide 12 evenly.

   A factor is a number that fits into another number a whole number of times. Test 1, 2, 3, 4, ... up to 12.

2. 2

   Factors of 12: 1, 2, 3, 4, 6, 12. That’s 6 factors total.

   1 × 12 = 12, 2 × 6 = 12, 3 × 4 = 12 — each multiplication pair gives two factors.

3. 3

   12 has more than two factors, so 12 is COMPOSITE.

   Anything with factors beyond just 1 and itself is composite.

4. 4

   Now 13. Try to find factors: 1 divides 13 (1 × 13 = 13). 2? No (13 is odd). 3? No (13 ÷ 3 isn’t whole). 4? No. 5? No. 6? No. Keep going — none work except 1 and 13 itself.

   You only need to test divisors up to √13 ≈ 3.6, so really just 2 and 3 — a Grade 4 shortcut to learn later.

5. 5

   13 has exactly two factors (1 and 13), so 13 is PRIME.

Common mistakes

• •Calling 1 a prime number. 1 has only ONE factor (itself), not two — so by definition it’s neither prime nor composite.
• •Calling 2 composite because "all even numbers are composite." 2 is actually the ONLY even prime — its only factors are 1 and 2.
• •Stopping the factor search too early — e.g. deciding 91 is prime because 2, 3, and 5 don’t divide it, missing that 91 = 7 × 13.
• •Confusing factors with multiples. Factors of 12 are 1, 2, 3, 4, 6, 12. Multiples of 12 are 12, 24, 36, 48, ... — completely different sets.

How Briveli teaches prime and composite numbers

Briveli teaches prime and composite numbers in Grade 4 with a build-up that starts from factor pairs and arrays, then moves into prime factorization in Grade 5 and 6 — used directly for greatest common factor and least common multiple problems.